[seqfan] Re: A002955: rooted trimmed trees

Neil Sloane njasloane at gmail.com
Mon Mar 2 18:38:19 CET 2015


> P.P.S.: should "free" be added to the names of
  sequences that are about free trees (like A000055)?

JJ, just to respond to your final question: my convention was always that
trees were unlabeled unless specified otherwise, and unrooted unless it
said rooted.

So by convention, "trees" meant unlabeled and unrooted.

Of course adding a comment to make the definition clearer does no harm.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Mon, Mar 2, 2015 at 11:55 AM, Joerg Arndt <arndt at jjj.de> wrote:

> I observe that this sequence (seems to) count
> "Unordered rooted trees without "x x" in the level
>  sequence for the pre-order walk."
>
> Here are those (8) trees for n = 6:
>
>    1:  [ 0 1 2 3 4 5 ]
> O--o--o--o--o--o
>
>    2:  [ 0 1 2 3 4 3 ]
> O--o--o--o--o
>       .--o
>
>    3:  [ 0 1 2 3 4 2 ]
> O--o--o--o--o
>    .--o
>
>    4:  [ 0 1 2 3 4 1 ]
> O--o--o--o--o
> .--o
>
>    5:  [ 0 1 2 3 2 3 ]
> O--o--o--o
>    .--o--o
>
>    6:  [ 0 1 2 3 2 1 ]
> O--o--o--o
>    .--o
> .--o
>
>    7:  [ 0 1 2 3 1 2 ]
> O--o--o--o
> .--o--o
>
>    8:  [ 0 1 2 1 2 1 ]
> O--o--o
> .--o--o
> .--o
>
>
> Now I realize that I do _not_ understand the comments.
> My understanding of "limb" is
> "the way (subtree) from a leaf towards the root until
>  the first branch point (which can be the root) is reached."
> Example: The tree
>   [ 0 1 2 3 4 2 1 2 1 ]
> O--o--o--o--o
>    .--o
> .--o--o
> .--o
> has limbs of lengths 4, 1, 2, and 1.
>
> Now from what I read in A002955 it should count
> trees without limbs of length 2 (? or length >= 2 ?).
> The trees I show above are(?) different, they avoid subtrees
>  *--o
>  .--o
>
> Can somebody clarify?
>
>
> Best regards,   jj
>
> P.S.: should "unordered" be added to the name?
> P.P.S.: should "free" be added to the names of
>   sequences that are about free trees (like A000055)?
>
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>


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